For every succeeding generation of integrated circuits, both transistor speed and transistor density has increased. To increase the transistor density, the metal line widths and spacing for the electrical interconnects have been reduced. The reduction of the spacing between the signal lines of an integrated circuit generally increases the capacitance between lines. This tends to make the lines noisier, as it is commonly called.
As the term is used herein, “integrated circuit” includes devices such as those formed on monolithic semiconducting substrates, such as those formed of group IV materials like silicon or germanium, or group III-V compounds like gallium arsenide, or mixtures of such materials. The term includes all types of devices formed, such as memory and logic, and all designs of such devices, such as MOS and bipolar. The term also comprehends applications such as flat panel displays, solar cells, and charge coupled devices.
When doing crosstalk or noise analysis, signal lines, also called nets, are identified as either victim nets or aggressor nets. The net being analyzed is considered the victim net, and those nets disposed adjacent to it, whether along its entire length or for just a portion of its length, are considered the aggressor nets. Nets that are not directly adjacent the victim net may also be considered as aggressor nets in the analysis of the victim net. The determination of what constitutes an aggressor net is outside of the scope of this discussion. When the analysis has been performed for a given victim net, then another net is selected as the new victim net, while the prior victim net may then be reclassified as an aggressor net, and the analysis is repeated for the new victim net.
The problem with such noise, and the importance of this type of analysis, continually increases as the voltage threshold for the active devices of integrated circuit is reduced, so as to speed up the integrated circuits. By lowering the voltage threshold of a transistor, and increasing the capacitance between nets, the probability increases that an amount of noise sufficient to switch the transistor state will be generated.
However, current noise analysis tools tend to be too pessimistic in their analysis, because they generally assumed that all aggressor nets will switch in the same direction, at the same time, and that their voltage peaks will be aligned. This results in a worst case maximum height composite noise waveform on the victim net. However, the number of aggressors that could have a significant amount of coupled noise to the victim net can often be quite large. In such a case, the likelihood of realizing a worst case composite noise, where all of the aggressor nets switch at exactly the same time, is very small. Because of the increasing complexity of integrated circuit designs, the problem of overestimating signal noise becomes more serious as the technology advances.
Two different general methods of noise analysis are typically used. The first is called a deterministic approach. In a deterministic approach, the noise waveform is estimated accurately by accounting for the logic and timing relationships between the aggressors and a victim. It is often necessary to perform static timing analysis and construct timing windows before this method of noise analysis can be performed. Although the incorporation of timing information in the noise analysis generally improves the accuracy of the noise estimation, it requires a very high computational effort.
The second method is called a probabilistic approach. In a probabilistic approach, it is assumed that the switching of the aggressor nets occurs randomly over a specific time interval within a clock period. Then the likelihood, or in other words the probability, that the total noise on a victim net will exceed a given threshold, such as the voltage threshold of a transistor on the victim net, is calculated. The mean time to failure is often used as a criterion to prioritize the jeopardy faced by victim nets that are subject to noise violation.
Unfortunately, the deterministic approach, as mentioned above, requires an extremely high computational effort, and therefore is not appropriate for a noise analysis of the entire integrated circuit. This leaves the probabilistic approach. However, there is no existing analytical model for probabilistic noise analysis, which makes it again computationally expensive.
An example of a probabilistic approach is presented in the paper Probabilistic Analysis of Interconnect Coupling Noise, by S. Vrudhula, et al., in the IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems, Vol. 22, No. 9, September 2003, pages 1188-1203. In that method, finding the mean time to failure for a given victim net requires an iterative search, which makes the method very slow and time consuming. Moreover, due to the lack of an analytical model, that method can only be used to computed the mean time to failure for a given noise threshold, and cannot compute the effective peak noise for a given mean time to failure.
What is needed, therefore, is a system that overcomes problems such as those described above, at least in part.